\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}

% internal field, delta-B
\begin{displaymath}
\alpha \cos\left(2\pi\nu t + \phi\pi/180\right) e^{-\lambda_{\rm T} t} + (1-\alpha) e^{-\lambda_{\rm L} t}
\end{displaymath}

% internal field, Gaussian broadened
\begin{displaymath}
\alpha \left[\cos(2\pi\nu t) -\frac{\sigma^2 t}{2\pi\nu}\sin(2\pi\nu t)\right] e^{-(\sigma t)^2/2} + (1-\alpha) e^{-(\lambda t)^\beta}
\end{displaymath}

% internal field, Lorentzian broadened
\begin{displaymath}
\alpha \left[\cos(2\pi\nu t) -\frac{a}{2\pi\nu}\sin(2\pi\nu t)\right] e^{-a t} + (1-\alpha) e^{-\lambda t}
\end{displaymath}

\end{document}